Eirikur's idea is a really good one. The only thing I'd add is that if you're going to define a column to store the reverse of the string, I'd do it as a persisted computed column. Then, when a row is INSERTed or UPDATEd, you won't have to worry about the new column - it'll be populated for you.
If you intend to use it in WHERE clauses, you could add a nonclustered index on it to cover your search queries. If it's the leading column in the index, you should be able to get index seeks.